An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
Mathematics of Computation
Spectral methods on triangles and other domains
Journal of Scientific Computing
From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex
SIAM Journal on Numerical Analysis
An analysis of the discontinuous Galerkin method for wave propagation problems
Journal of Computational Physics
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Discrete Dispersion Relation for hp-Version Finite Element Approximation at High Wave Number
SIAM Journal on Numerical Analysis
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
Journal of Computational Physics
A Discontinuous Galerkin Method for Linear Symmetric Hyperbolic Systems in Inhomogeneous Media
Journal of Scientific Computing
Journal of Scientific Computing
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Dispersive and Dissipative Behavior of the Spectral Element Method
SIAM Journal on Numerical Analysis
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Here, we solve the time-dependent acoustic and elastic wave equations using the discontinuous Galerkin method for spatial discretization and the low-storage Runge-Kutta and Crank-Nicolson methods for time integration. The aim of the present paper is to study how to choose the order of polynomial basis functions for each element in the computational mesh to obtain a predetermined relative error. In this work, the formula 2p+1~@khk, which connects the polynomial basis order p, mesh parameter h, wave number k, and free parameter @k, is studied. The aim is to obtain a simple selection method for the order of the basis functions so that a relatively constant error level of the solution can be achieved. The method is examined using numerical experiments. The results of the experiments indicate that this method is a promising approach for approximating the degree of the basis functions for an arbitrarily sized element. However, in certain model problems we show the failure of the proposed selection scheme. In such a case, the method provides an initial basis for a more general p-adaptive discontinuous Galerkin method.